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Constructing exactly conservative scheme in a non-conservative form. (English) Zbl 0959.65097

A non-conservative scheme that guarantees exact mass-conservation is proposed. This scheme has been tested by linear advection with variable velocity field and Burgers’ equation. The proposed scheme can provide a useful tool to solve nonlinear equations in a non-conservative representation which has been proved to be quite stable for multiphase flow calculations.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35Q53 KdV equations (Korteweg-de Vries equations)
76M20 Finite difference methods applied to problems in fluid mechanics
76T30 Three or more component flows
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